IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p760-d759929.html
   My bibliography  Save this article

Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

Author

Listed:
  • Ibrahim Elbatal

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Naif Alotaibi

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Salem A. Alyami

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Mohammed Elgarhy

    (The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt)

  • Ahmed R. El-Saeed

    (Department of Basic Sciences, Obour High Institute for Management & Informatics, Obour 11848, Egypt)

Abstract

This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.

Suggested Citation

  • Ibrahim Elbatal & Naif Alotaibi & Salem A. Alyami & Mohammed Elgarhy & Ahmed R. El-Saeed, 2022. "Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:760-:d:759929
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/760/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/760/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Devendra Kumar & Sanku Dey & Saralees Nadarajah, 2017. "Extended exponential distribution based on order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9166-9184, September.
    2. Haghighi, Firoozeh, 2014. "Optimal design of accelerated life tests for an extension of the exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 251-256.
    3. N. Balakrishnan & Donghoon Han & G. Iliopoulos, 2011. "Exact inference for progressively Type-I censored exponential failure data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 335-358, May.
    4. Sanku Dey & Chunfang Zhang & A. Asgharzadeh & M. Ghorbannezhad, 2017. "Comparisons of Methods of Estimation for the NH Distribution," Annals of Data Science, Springer, vol. 4(4), pages 441-455, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mahmoud R. Mahmoud & Hiba Z. Muhammed & Ahmed R. El-Saeed, 2023. "Inference for Generalized Inverted Exponential Distribution Under Progressive Type-I Censoring Scheme in Presence of Competing Risks Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 43-76, February.
    2. van Bentum, Thomas & Cramer, Erhard, 2019. "Stochastic monotonicity of MLEs of the mean for exponentially distributed lifetimes under hybrid censoring," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 1-8.
    3. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.
    4. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    5. Devendra Kumar & Neetu Jain & Mazen Nassar & Osama Eraki Abo-Kasem, 2021. "Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application," Annals of Data Science, Springer, vol. 8(4), pages 785-811, December.
    6. repec:exl:29stat:v:20:y:2019:i:3:p:57-80 is not listed on IDEAS
    7. Cai, Xia & Tian, Yubin & Ning, Wei, 2019. "Change-point analysis of the failure mechanisms based on accelerated life tests," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 515-522.
    8. Devendra Kumar & Maneesh Kumar & J. P. Singh Joorel, 2022. "Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data," Annals of Data Science, Springer, vol. 9(4), pages 723-748, August.
    9. Malik Mansoor Rashid & Kumar Devendra, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 57-79, September.
    10. Mansoor Rashid Malik & Devendra Kumar, 2017. "Relations For Moments Of Progressively Type-Ii Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.
    11. Mansour Shrahili & Naif Alotaibi & Devendra Kumar & Salem A. Alyami, 2020. "Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    12. Malik Mansoor Rashid & Kumar Devendra, 2017. "Relations for Moments of Progressively Type-II Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.
    13. Mansoor Rashid Malik & Devendra Kumar, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 57-79, September.
    14. Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    15. Moustafa, Kassem & Hu, Zhen & Mourelatos, Zissimos P. & Baseski, Igor & Majcher, Monica, 2021. "System reliability analysis using component-level and system-level accelerated life testing," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    16. Samir K. Ashour & Ahmed A. El-Sheikh & Ahmed Elshahhat, 2022. "Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 885-923, August.
    17. Abd El-Raheem M. Abd El-Raheem & Mona Hosny & Mahmoud H. Abu-Moussa, 2021. "On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    18. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
    19. Mugnaini, Marco & Addabbo, Tommaso & Fort, Ada & Elmi, Alessandro & Landi, Elia & Vignoli, Valerio, 2020. "Magnetic brakes material characterization under accelerated testing conditions," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    20. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    21. Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:760-:d:759929. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.